Fluorescence spectroscopy is a nondestructive optical method extensively used to probe complex biological systems, including cells and tissues for biochemical, functional and morphological changes associated with pathological conditions. Such approaches have potential for noninvasive diagnosis in vivo. Fluorescence measurements can be categorized as either static (steady-state or time-integrated) or dynamic (time-resolved). While steady-state techniques provide an integrate spectrum over time that gives information about fluorescence emission intensity and spectral distribution, time-resolved techniques measure the dynamically evolving fluorescence emission, providing additional insight into the molecular species of the sample (e.g., the number of fluorescence species and their contribution to the overall emission), and/or changes in the local environment.
Two methods for time-resolved fluorescence measurements are widely used: the time-domain and the frequency-domain. For time-domain, the sample is excited with a short pulse of light (typically nanosecond or shorter), and the emission intensity is measured following excitation with a fast photodetector. In the frequency-domain, an intensity-modulated light induces the sample fluorescence. Due to the fluorescence relaxation lifetime of the sample, the emitted wave is delayed in time relative to the excitation, inducing a phase-shift, which is used to calculate the decay time.
In the context of time-domain measurements, the fluorescence Impulse Response Function (IRF) contains all the temporal information of a single fluorescence decay measurement. The IRF is the system response to an ideal d-function excitation. In practice, the excitation light pulses are, typically, at least several picoseconds wide. Thus they should be taken as a train of d-functions with different amplitudes; each one initiating an IRF from the sample, with intensity proportional to the height of the d-function. The measured intensity decay function is the sum of all IRFs starting with different amplitudes and at different times. Mathematically, the measured fluorescence intensity decay data is given by the convolution of the IRF with the excitation light pulse. Thus, to estimate the fluorescence IRF of a compound, the excitation light pulse must be deconvolved from the measured fluorescence intensity pulse.
When the excitation light pulse is sufficiently short, resembling a d-function excitation, the measured fluorescence decay would closely resemble the intrinsic IRF. Currently, very short (femtoseconds) excitation light pulses can be generated; although for their lack of general availability, picosecond lasers are still the most widely used light sources for time-resolved measurements. Therefore, in many cases the intrinsic fluorescence IRF of the investigated compounds will have lifetimes on the order of the excitation light pulse width, and subsequently, an accurate deconvolution technique becomes crucial.
Deconvolution methods are usually divided into two groups: those requiring an assumption of the functional form of the IRF, such as the nonlinear least-square iterative reconvolution method, and those that directly give the IRF without any assumption, such as the Fourier and Laplace transform methods, the exponential series method, and the stretched exponential method, among others. In addition to these methods, an alternative approach known as global analysis, in which simultaneous analysis of multiple fluorescence decay experiments are performed, has proven useful for both time- and frequency-domain data. Among these methods, however, the most commonly used deconvolution technique is the nonlinear least-square iterative reconvolution (LSIR) method. This technique applies a least-squares minimization algorithm to compute the coefficients of a multi-exponential expansion of the fluorescence decay. In complex biological systems, fluorescence emission typically originates from several endogenous fluorophores and is affected by light absorption and scattering. From such a complex medium, however, it is not entirely adequate to analyze the time-resolved fluorescence decay transient in terms of a multi-exponential decay, since the parameters of a multi-exponential fit of the fluorescence IRF cannot readily be interpreted in terms of fluorophore content. Moreover, different multi-exponential expressions can reproduce experimental fluorescence decay data equally well, suggesting that for complex fluorescence systems there is an advantage in avoiding any a priori assumption about the functional form of the IRF decay physics.
Similarly, in the context of fluorescence lifetime imaging microscopy (FLIM), the deconvolution method is critical to data analysis. FLIM has become increasingly popular due to its ability to distinguish fluorophores differing in lifetime but with similar spectral features. Most current methods of FLIM analysis require the assumption that the excitation pulses are negligibly short, so that the fluorescence emission can be approximated to the intrinsic fluorescence decay or IRF and that the IRF follows a monoexponential decay law. However, the required assumptions of a short excitation pulse and of a single exponential fluorescence decay cannot often be fulfilled in practice, where most laser excitation pulses are several picoseconds wide and multiple fluorophores in the same specimen are simultaneously excited. Under these conditions, a deconvolution algorithm needs to be applied and a more general fluorescence decay law needs to be assumed.
Further, because fluorescence lifetimes in imaging are determined on a pixel-by-pixel basis, iterative methods for recovering the time decays can be time consuming and generally require the acquisition of a considerable number of data samples.
Expansion on the discrete time Laguerre basis as a way of deconvolving the intrinsic properties of a dynamic system from experimental input-output data was initially proposed by Marmarelis, and applied to linear and nonlinear modeling of different physiological systems including renal auto-regulation and autonomic control of heart rate. A Laguerre based deconvolution technique was recently reported as a variant of the LSIR technique, in which the fluorescence IRF is expressed as an expansion on the discrete time Laguerre basis instead of a weighted sum of exponential functions. The Laguerre deconvolution technique has been previously applied to optical spectroscopy of tissues with promising results to the analysis of time-resolved fluorescence emission data from atherosclerotic lesions, and temporal spread functions of transmitted ultrafast laser pulses through different types of human breast tissue. Further, in Marcu et al., U.S. Pat. No. 6,272,376, which is incorporated by reference herein in its entirety as if fully set forth, the Laguerre deconvolution technique was applied to time-resolved, laser-induced fluorescence spectroscopy (TR-LIFS) and used to characterize tissue by investigating the fluorescence response of protein and lipid fluorophore components in both spectral and time domains. However, a formal evaluation of this technique, as it applies to fluorescence measurements, has not been reported.
Accordingly, a need exists for methods and systems for the quantitative and qualitative analysis of time resolved fluorescence emission data and fluorescence lifetime imaging microscopy data which are both accurate and quick.